Schoen's Hybrid Triply Periodic Minimal Surfaces

This page presents several families of
triply periodic minimal surfaces that
may be viewed as combinations of other
surfaces. A common way to conceptualize them is to view them as a central
body in a polyhedron with tunnels extending out to various faces, edges,
or vertices.

S'-S"
The unit cell is a square box with tunnels to the top and bottom of the box
and to the vertical edges. The box cannot be a cube; this shows the maximum
height box in which the surface exists. For lower boxes, two surfaces exist,
one with a narrower neck top and bottom and one with a wider neck. Genus 4.
Evolver file:
SSadj.fe

P
Schwarz' P surface, included here for reference. The unit cell is
a cube, and tunnels extend to each face. Genus 3.
Evolver file:
pcell.fe

S'-S"|P
This surface can be viewed as S'-S" with P-type tunnels coming out of the top
and bottom necks. Actually a 1-parameter family in the ratio of the
sizes of the necks. Genus 6.
Evolver file:
pssadj.fe

H'-T
This surface may be viewed as narrow tunnels to the sides of a hexagonal
prism, with wide tunnels to the top and bottom.
Genus 4.
Evolver file:
HTadj.fe

H"-R
This surface may be viewed as narrow tunnels to the vertical
edges of a hexagonal
prism, with wide tunnels to the top and bottom.
Genus 5.
Evolver file:
HRadj.fe

T'-R'
This surface may be viewed as a central body with tunnels to the sides
of a hexagonal
prism, and those tunnels merged vertically.
Genus 6.
Evolver file:
TRadj.fe

H'-T|H"-R
A hexagonal prism with narrow tunnels to both vertical faces and
vertical edges. Ratio of sizes of necks can be varied. Genus 8.
Evolver file:
HRHTadj.fe

T'-R'|H'-T
A central body in a hexagonal prism with tunnels out to the vertical faces,
and those tunnels connected vertically. Or T'-R' with catenoid holes
punched through certain places. Ratio of sizes of necks can be varied.
Genus 9.
Evolver file:
HTTRadj.fe

H"-R|T'-R'
A central body in a hexagonal prism with tunnels out to the vertical edges,
and those tunnels connected vertically. Ratio of sizes of necks can be varied.
Genus 10.
Evolver file:
TRHTadj.fe